Rhythmic signals or rhythms are generated by various sources. Within the context of the following description, a rhythm, is defined as any modulation, fluctuation or recurrent pattern of activity within a signal or derivative thereof that has a measureable frequency or frequency range associated with it, and a duration of at least two or more cycles as defined by the time interval of recurrence, which itself may be variable over time.
Neural rhythms are associated with different brain functions and pathological conditions. The non-stationary nature of neural rhythms makes them difficult to detect and isolate. The intricate texture of neural recordings, which are interwoven with time-varying rhythmicities, nonlinearities, random fluctuations and artifacts, presents a considerable challenge for signal analysis. Observation of certain features may be crucial for clinical monitoring or diagnosis. For instance, the relative power and coherence of the delta, theta, alpha or gamma band rhythms can be related to different functional states of the brain. Other abnormal rhythmic features, such as high-frequency (>100 Hz) oscillations, have been implicated in neurological disorders such as epilepsy and Parkinson's disease. Therefore, robust separation of signal features based on rhythmicity is not only desirable but necessary.
Fourier transform methods are ill-suited to deal with non-stationary signals. As an alternative, the wavelet transform has proven itself to be versatile and effective, with improved ability to resolve signal features in both the time and frequency domains.
In the continuous wavelet transform, the input signal is convolved with a mother wavelet that is infinitely scalable and translatable. This generates an arbitrary wavelet basis for signal representation. The resulting analysis is computationally intensive with inherent redundancy in the wavelet coefficients, and exact reconstruction of the input signal is not possible for non-orthogonal bases. The discrete wavelet transform (DWT) eliminates redundancy by using an orthogonal or biorthogonal wavelet basis, usually with dyadic scaling and translation. The wavelet basis is used to formulate a finite impulse response quadrature mirror filter-bank for signal decomposition and reconstruction. The DWT therefore allows for multi-resolution analysis, which is superior to conventional filtering methods for isolating rhythms, because multi-resolution analysis subdivides and covers the time-frequency plane, whereas single-stage finite infinite response or infinite impulse response filters are limited in bandwidth and resolve frequencies but not temporal features. The discrete wavelet packet transform (DWPT or WPT) is an extension of the discrete wavelet transform (DWT) and enables greater frequency resolution of the input signal, especially at higher frequencies, where the resolution of the DWT is not as good.
The manner in which the time-frequency plane is subdivided by wavelet or wavelet packet transform-based multi-resolution analysis is dependent on the selection of the discrete wavelet or wavelet packet basis functions. The selection of the appropriate basis is related to the intended application of the analysis procedure.
Coefficient-thresholding basis selection methods have been developed for data compression and signal de-noising applications, including minimization of Stein's unbiased risk estimate (SURE), as discussed in the publication entitled “Adapting to unknown smoothness via wavelet shrinkage” authored by Donoho et al., Journal of the American Statistical Association, 90:1200-1224, 1995, and empirical Bayes estimates, as discussed in the publication entitled “Adaptive wavelet thresholding for image de-noising and compression” authored by Chang et al., IEEE Transactions on Image Processing, 9(9):1532-1546, 2000. However, such methods assume statistical properties of the observed data that cannot be intrinsically verified, but only estimated, including the nature and underlying distribution of the noise or wavelet coefficients. Also, the choice of wavelet basis functions and the order of decomposition are left to the user, and these can affect the performance of the estimators. Furthermore, none of the aforementioned techniques are specific to the task of detecting and isolating/extracting rhythmic features from a given input signal.
It is therefore an object of the present invention to provide a novel method and rhythm extractor for detecting and isolating rhythmic signal features from an input signal.